Question

Let us suppose that the body weights of 800 students have a normal

distribution with mean l = 66 kg and standard deviation r = 5 kg.

Find the number of students whose weight is:

a) between 65 and 75 kg;

b) over 72 kg

Answer 1

X ~ $N(66, 5^2)$

a) $P(65<X<75)=P(65<N(66,5^2)<75)=P(65<66+5N(0,1)<75)=P(-0.2<N(0,1)<1.8)=0.96407-0.42074=0.54333$

So, there are $0.54333*800=434.664\approx435$ students have such weight

b) $P(X>72)=P(N(66,5^2)>75)=P(66+5N(0,1)>72)=P(N(0,1)>1.2)=0.11507$

So, there are $0.11507*800=92.056\approx92$ students have such weight